I have tried all kinds of different configurations (starting with the one recommended in the linked S/O answer above). Finally, in an act of desperation, I set it to this, which I thought would make it try to compress all requests (everything except */* commented out):

What can be preventing the GZIP from being applied to my Web API methods?

Update

I have since tried both the NuGet Web API Compression package, and editing the applicationHost.config in both IIS Express 8.0 (Visual Studio) and a locally-installed IIS 7.5. All have yielded the same results: requests for other mime types like text/* work, but application/json refuses to be gzipped.